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Published online by Cambridge University Press: 12 March 2014
We set  = ‹
 = ‹ , ≤L , # ›, where
, ≤L , # ›, where  is the set of degrees of nonconstructibility for countable sets of countable ordinals. We show how to define inductively over this structure the degrees of such sets of ordinals in Κ, the core model, and the next few core models thereafter, i.e. without reference to mice, premice or measurable cardinals
 is the set of degrees of nonconstructibility for countable sets of countable ordinals. We show how to define inductively over this structure the degrees of such sets of ordinals in Κ, the core model, and the next few core models thereafter, i.e. without reference to mice, premice or measurable cardinals